Civil Engineering Reference
In-Depth Information
Y
y
x
y
0
x
l
y
l
d
α
c
x
0
X
b
a
Figure 4.2.
Example 4.1 Rotation,
a
.
axcos
bysin
cycos
dxsin
xabxcos ysin
ycd
=
=
=
=
=+=
a
a
a
a
0
0
0
0
a
+
a
l
0
0
=−
=
ycos
a
−
xsin
a
l
0
0
zz
l
=
0
The equations for
x
,
y
, and
z
can be represented in matrix form as follows:
cos sin
sin os
a
a
0
0
x
y
z
x
y
z
o
l
−
a
a
=
(4.1)
o
l
0
0
1
o
l
Example 4.2
Rotation matrix,
b
Derive the beta,
b
, rotation matrix.
The following variables are represented in Figure 4.3 and are used to
develop
b
. The location of
y
remains unchanged since rotation is occurring
about that axis.
b
= rotation about global
Y
axis from the global to the local system
(
x
0
,
z
0
) = global coordinate location
(
x
l
,
z
l
) = local coordinate location
axcos
bzsin
czcos
dxsin
=
=
=
=
b
b
b
b
0
0
0
0
